Find the coordinates of points on the unit circle corresponding to an angle $ heta$ in a flipped configuration.

Given a unit circle, we need to find the coordinates of points corresponding to the angle $\theta = \frac{5\pi}{4}$, but with the configuration flipped over the x-axis.

In the standard unit circle, the point corresponding to $\theta = \frac{5\pi}{4}$ is:

$\left(\cos \frac{5\pi}{4}, \sin \frac{5\pi}{4}\right)$

Using the trigonometric values:

$\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$

Since the configuration is flipped over the x-axis, we change the sign of the y-coordinate:

$\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$

Thus, the coordinates are:

$\boxed{\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}$

Consider the flipped unit circle and the angle $ heta = frac{5pi}{4}$.

Normally, the coordinates on the unit circle are:

$left(cos frac{5pi}{4}, sin frac{5pi}{4}
ight)$

Evaluating this, we get:

$left(-frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight)$

With the flipped configuration over the x-axis, we invert the y-coordinate’s sign:

$left(-frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$

Hence, the coordinates in the flipped configuration are:

$oxed{left(-frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)}$

Flipped unit circle with angle $ heta = frac{5pi}{4}$.

Original coordinates:

$left(-frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight)$

After flipping over the x-axis:

$left(-frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$

Result:

$oxed{left(-frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)}$

Start Using PopAi Today